Spectral properties of a certain class of Carleman operators

S. M. Bahri

Address. Department of Mathematics, University of Mostaganem, BP 227, Mostaganem, 27000, Algeria

E-mail: bahrisidimohamed@univ-mosta.dz

Abstract. The object of the present work is to construct all the generalized spectral functions of a certain class of Carleman operators in the Hilbert space $ L^{2}( X,\mu ) $ and establish the corresponding expansion theorems, when the deficiency indices are (1,1). This is done by constructing the generalized resolvents of $A$ and then using the Stieltjes inversion formula.

AMSclassification. Primary 05C38, 15A15; Secondary 05A15, 15A18.

Keywords. Spectral theory, integral operator, defect indices.